Why Math Is the Best Way to Make Sense of the World

When Rebecca Goldin spoke to a recent class of incoming freshmen at George Mason University, she relayed a disheartening statistic: According to a recent study, 36 percent of college students don’t significantly improve in critical thinking during their four-year tenure. “These students had trouble distinguishing fact from opinion, and cause from correlation,” Goldin explained.

She went on to offer some advice: “Take more math and science than is required. And take it seriously.” Why? Because “I can think of no better tool than quantitative thinking to process the information that is thrown at me.” Take, for example, the study she had cited. A first glance, it might seem to suggest that a third of college graduates are lazy or ignorant, or that higher education is a waste. But if you look closer, Goldin told her bright-eyed audience, you’ll find a different message: “Turns out, this third of students isn’t taking any science.”

Goldin, a professor of mathematical sciences at George Mason, has made it her life’s work to improve quantitative literacy. In addition to her research and teaching duties, she volunteers as a coach at math clubs for elementary- and middle-school students. In 2004, she became the research director of George Mason’s Statistical Assessment Service, which aimed “to correct scientific misunderstanding in the media resulting from bad science, politics or a simple lack of information or knowledge.” The project has since morphed into STATS (run by the nonprofit Sense About Science USA and the American Statistical Association), with Goldin as its director. Its mission has evolved too: It is now less of a media watchdog and focuses more on education. Goldin and her team run statistics workshops for journalists and have advised reporters at publications including FiveThirtyEight, ProPublica and The Wall Street Journal.

When Quanta first reached out to Goldin, she worried that her dual “hats” — those of a mathematician and a public servant — were too “radically different” to reconcile in one interview. In conversation, however, it quickly became apparent that the bridge between these two selves is Goldin’s conviction that mathematical reasoning and study is not only widely useful, but also pleasurable. Her enthusiasm for logic — whether she’s discussing the manipulation of manifolds in high-dimensional spaces or the meaning of statistical significance — is infectious. “I love, love, love what I do,” she said. It’s easy to believe her — and to want some of that delight for oneself.

Quanta Magazine spoke with Goldin about finding beauty in abstract thought, how STATS is arming journalists with statistical savvy, and why mathematical literacy is empowering. An edited and condensed version of the conversation follows.

Where does your passion for mathematics and quantitative thought come from?

As a young person I never thought I liked math. I absolutely loved number sequences and other curious things that, in retrospect, were very mathematical. At the dinner table, my dad, who is a physicist, would pull out some weird puzzle or riddle that sometimes only took a minute to solve, and other times I’d be like, “Huh, I have no idea how that one works!” But there was an overall framework of joy around solving it.

When did you recognize you could apply that excitement about puzzles to pursuing math professionally?

Actually very late in the game. I was always very strong in math, and I did a lot of math in high school. This gave me the false sense that I knew what math was about: I felt like every next step was a little bit more of the same, just more advanced. It was very clear in my mind that I didn’t want to be a mathematician.

But when I went to college at Harvard, I took a course in topology, which is the study of spaces. It wasn’t like anything I’d seen before. It wasn’t calculus; it wasn’t complex calculations. The questions were really complicated and different and interesting in a way I had never expected. And it was just kind of like I fell in love.

You study primarily symplectic and algebraic geometry. How do you describe what you do to people who aren’t mathematicians?

One way I might describe it is to say that I study symmetries of mathematical objects. This comes about when you’re interested in things like our universe, where the Earth is rotating, and it’s also rotating around the sun, and the sun is in a larger system that is rotating. All those rotations are symmetries. There are a lot of other ways symmetries come up, and they can get really, really complicated. So we use neat mathematical objects to think about them, called groups. This is useful because if you’re trying to solve equations, and you know you have symmetries, you can essentially find a way mathematically to get rid of those symmetries and make your equations simpler.